Question

The Hi-Lo game is a four-player game played in six rounds. In every round, each player chooses to bid Hi or Lo. The bids are made simultaneously. If all four bid Hi, then all four lose 1 point each. If three players bid Hi and one bids Lo, then the players bidding Hi gain 1 point each and the player bidding Lo loses 3 points. If two players bid Hi and two bid Lo, then the players bidding Hi gain 2 points each and the players bidding Lo lose 2 points each. If one player bids Hi and three bid Lo, then the player bidding Hi gains 3 points and the players bidding Lo lose 1 point each. If all four bid Lo, then all four gain 1 point each.
Four players Arun, Bankim, Charu, and Dipak played the Hi-Lo game. The following facts are known about their game:
1.At the end of three rounds, Arun had scored 6 points, Dipak had scored 2 points, Bankim and Charu had scored -2 points each.
2.At the end of six rounds, Arun had scored 7 points, Bankim and Dipak had scored -1 point each, and Charu had scored -5 points.
3.Dipak’s score in the third round was less than his score in the first round but was more than his score in the second round.
4.In exactly two out of the six rounds, Arun was the only player who bid Hi.
In how many rounds did Dipak gain exactly 1 point? [This Question was asked as TITA]

• A. 1 round
• B. 3 rounds
• C. 2 rounds
• D. 5 rounds

Answer 1

The Correct Option is A

Dipak gained exactly 1 point in 1 round.

Answer 2

Dipak's score in the first round increased by 3 points, and his score in the third round decreased by 1 point.
Therefore, there must be a round in which Dipak's score increased by exactly 1 point.
Given that Dipak's score after the third round was 2 points and his score after the sixth round was -1 point, there must be a round where his score increased by 1 point.
Thus, Dipak gained exactly 1 point in 1 round.